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# Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0

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Joined: 23 Feb 2015
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Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0  [#permalink]

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Updated on: 07 Jun 2019, 03:33
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Difficulty:

85% (hard)

Question Stats:

51% (01:58) correct 49% (02:11) wrong based on 38 sessions

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Is $$2-x<√(4-x^2)?$$

(1) $$x^2<4$$
(2) $$x>0$$

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Originally posted by Asad on 01 Apr 2019, 09:18.
Last edited by Bunuel on 07 Jun 2019, 03:33, edited 1 time in total.
Edited the OA.
Senior Manager
Joined: 13 Feb 2018
Posts: 496
GMAT 1: 640 Q48 V28
Re: Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0  [#permalink]

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01 Apr 2019, 10:00
1
Working on question stem:
1) after squaring both sides we get (2-x)(2-x)<(2-x)(2+x)
2) after subtrackting we get: (2-x)(2-x)-(2-x)(2+x)<0
3) after factoring out 2-x we get: (2-x)(2-x-(2+x))<0
4) after simplification we get: 2$$x^2$$-4x<0
5) working further: x=0; x=2
6) range: 0<x<2

1 stm: -2<x<2 not sufficient
2 stm: x>0 not suff

Both statements: 0<x<2 sufficient

IMO
Ans: C
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Re: Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0  [#permalink]

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07 Apr 2019, 05:57
1
Is $$2-x<√(4-x^2)?$$
1) $$x^2<4$$
2) $$x>0$$

IMO, ans should be C.

Considering only statement 2 (as per the OA), if $$x=3$$, then
$$2-3<\sqrt{4-9}$$
Here comes the concept of complex number which is not valid for GMAT.

Hence, OA should C ($$0<x<2$$)
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Re: Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0  [#permalink]

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07 Apr 2019, 06:09
B is not correct .

for x = 1 , it is true

but for x= 2 , it is false

0<0 not possible

but when we combine both,

we eliminat2 and we restrict the values between -2 and 2

So It should be C

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Re: Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0  [#permalink]

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07 Apr 2019, 09:03
What I feel is... In Statement B ,X can take Values between 0 and 2..
0<X<2...

Here's why..

Look at RHS... Sqrt (4-x^2)
Now we all know that GMAT doesn't want us to take Sqrt of a negative value...

If i take X = 1
2-1 = 1 (LHS)
Sqrt (4-x^2) = 1.73
RHS > LHS , a definite yes

Let's take X = 1.5

2-1.5 = 0.5
Sqrt (4-x^2) = 1.33

RHS>LHS , again a definite yes..

Now the reason why I'm not willing to consider X = 2 is because I believe GMAT considers square root of positive numbers... Taking X= 2 will make RHS 0 And zero is neither negative nor positive..

I don't know whether my reasoning is right or wrong. . experts?? Might need your help ..

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Posts: 945
Re: Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0  [#permalink]

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07 Jun 2019, 03:29
Is $$2-x<√(4-x^2)?$$
1) $$x^2<4$$
2) $$x>0$$

After simplification of the stem, the question is asking 0< x<2

1) -2< x < 2, Not Suff.

2) x could be in the range 0< x<2 or not. Not Suff.

1+2

x is in the range 0< x<2, Suff.

Ans C
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Re: Is 2 - x < √(4 - x^2)? (1) x^2 < 4 (2) x > 0   [#permalink] 07 Jun 2019, 03:29
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